As shown in FIG. 1, focused ion beam systems typically contain a needle type source 1, a condenser lens 2, a mid-column deflector system 3, and an objective lens system 4. The condenser lens system typically contains electrodes 8, 9, 10 forming individual lenses 5, 6 located inside a vacuum chamber 7. The objective lens forms a finely focused beam into a spot 12. Electron microscopes have achieved atomic scale resolution, but instruments based on ion beams have not been able to achieve such small focii. The typical helium microscope consists of a needle-type ion source and round electrostatic lenses. These lenses suffer from the defect of chromatic aberration, which causes enlargement of the focal spot as the lens aperture is opened. At the aperture size where the brightness limit (for 0.5 pA current) and spherical aberration each contribute 0.1 nm of aberration, chromatic aberration dominates with a contribution of 1.0 nm [R. Hill, F. H. M. Faridur Rahman, Nucl. Instr. and Meth. in Phys. Res. A645 (2011) 96: FIG. 1]. Chromatic aberration also dominates the aberration of typical focused ion beam systems based on electrostatic objective lenses, causing the current available in a focal spot of fixed size to fall as the cube of the ion energy.
Fortunately if round lenses are not used, an achromatic system can be configured sing an objective lens consisting of a pair 14, 16 of interleaved quadrupole lenses of the Kelman-Yavor type. These lenses have 8 poles, with alternating electric and magnetic poles, and if the magnetic poles are electrically isolated [Martin and Goloskie, Applied Physics Letters 40 (1982) 191], they can be excited with voltages that create cos(t) [dipole}, cos(2t) [quadrupole}, cos(3t) [hexapole} or cos(4t) [octopole} potentials. The magnetic poles produce a magnetic force field (q v×B) which is collinear with the electric force field (qE) at each point inside the lens, oppositely directed to the electric force, and twice its magnitude. Under these conditions the variation of the focal length with ion energy is zero, and chromatic aberration of the lens is eliminated. Two such interleaved lenses adjusted so that their principal sections are in the same plane constitute an objective lens focusing in both x and y principal sections. When two such lenses 14, 16 are combined with an electrostatic condensing lens 2 to form a particle-optical column, the quadrupoles may also be operated at different electric to magnetic ratios which cancel the chromatic aberration of the whole column rather than only the lenses [Martin PCT/US94/13358].
As pointed out by Crewe [Crewe, Eggenberger, Welter & Wall, J. Appl. Phys 38 (1967) 4257], the unequal magnifications of a doublet in its two principal sections do not matter for a scanning microscope, where the squareness of the image is determined by the scanning system rather than the probe-forming objective lens. This is particularly true for the atom-emitter source used in helium microscopes, where the geometrical image of the source is likely to be smaller than the aberrations caused by the objective lens.
Both round lenses and quadrupole lenses suffer from aperture aberrations. In a round lens the diameter of the focal spot increases with the cube of the aperture radius, rather than with the linear increase characteristic of chromatic aberration, and has a single “spherical” aberration coefficient Cs. A perfectly symmetrical quadrupole lens has three intrinsic coefficients A, C, E of the formx3=Aa3+3Cab2,  (1)y3=3Ca2b+Eb2  (2)where (x3,y3) is the aberration at the image, and (a,b) are the paraxial angles of convergence of rays to the image (in effect a measure of the diameter of the beam in the lens aperture).
The usefulness of all types of lenses is limited by the mechanical tolerances with which they can be manufactured. These tolerances produce parasitic aberrations which add to the intrinsic aberrations at the focus. Round lenses are finished with lapping compound and measured on air-bearing rotary tables [Orloff, Utlaut, and Swanson, isbn 0-306-47350-x (Kluwer, 2003, p. 163]. Even then they require stigmation, which involves adding dipole and quadrupole potentials to the mid-column deflectors 11,13 located between the ion source and the objective lens (ibid., p 161). In quadrupole lenses the tolerance on placement of the individual poles corresponds to the ellipticity of round lenses. For a single quadrupole lens, an estimate of the 3rd-order parasitic aberration coefficient G produced when the four poles deviate by amounts P from the average radius R isG=4P(T/R)3,  (3)where T is the throw distance to one of its astigmatic line images. The aberration itself may be estimated asx3=Gb3=4P(T/R)3(dR/T)3=4P(dR/R)3  (4)where b=dR/T is the semi-angle of convergence of the beam at its focus, when the beam occupies a fraction dR/R of the lens radius. For a typical tolerance P=1 micron and dR/R=0.1, the parasitic aberration is thus 1 nanometer. Apparently the lens must be stopped down to limit parasitic aberrations, and the benefits of chromatic correction are therefore limited.
The 8 poles of an interleaved lens can be used to eliminate this problem by introducing compensation of its 3rd order parasitic aberrations. The combined effect of 8 deviations is to produce an octopole potential which may be at an arbitrary rotational angle around the lens axis, rather than being aligned with the principal sections of the quadrupole lens. The misalignment can be described as a sum of a “normal octopole” of unknown magnitude with radial form cos(4t) and its maxima lying in the principal sections of the quadrupole lens, and a second “skew octopole” of unknown magnitude with radial form sin(4t) and a rotation by 22.5 degrees with respect to the normal one. For the quadrupole doublet, there are thus four unknown octopole strengths (Uoc Uos) and (Doc, Dos) where U and D represent the upstream and downstream lenses and c,s the cosine and sine terms.
By computing the deflections caused by these fields it can be shown [Martin and Goloskie, Nuclear Instruments and Methods B104 (1995) 59-63] that the quadrupole doublet has five third-order coefficients A thru E with the formx3=Aa3+3Ba2b+3Cab2+Db3=(1.0a3−0.3a2b+2.4ab2+21.8b3)v4  (5)y3=Ba3+3Ca2b+3Dab2+Eb3=(−0.3a3+2.4a2b+21.8ab2−238b3)v4  (6)where A, C, E result from the normal octopole and B, C from the skew one. The numerical values listed above are relative strengths for four equal parasites in a lens of typical dimensions. These relative values are computable functions of the unknown strengths, for example<x/ab2>=3C=−3(Uoc/(p2q2)−Doc)v4  (7)<y/b3>=E=−(Uoc/q4−Doc)v4  (8)where v is the final object distance from the downstream lens and p,q are the run-out (p>1) and run-in (q<1) ratios of rays in the x and y sections. These relations show that D and E are the dominant coefficients, and that the upstream lens with octopole strengths (Uoc, Uos) is the major source of aberrations.
As was written in 1970, “One of the main mechanical problems of quadrupole systems arises from the large number of pole pieces or electrodes that must be aligned; it is clear that if all the octopole effects could be obtained by exciting the electrostatic lenses asymmentrically . . . this problem would be greatly simplified” [Hawkes, Quadrupoles in Electron Lens Design, (Academic Press, NY 1970): p. 353]. It is an object of the present invention to show how regular symmetric (rather than asymmetric) excitations can be applied to eliminate parasitic aberrations, and thereby obtain improved resolution from quadrupole lenses.